I have a dataset that is a range of numbers between 40-600 [40,41,...600]. I then create 3 buckets of values from that range.
bucket 1: [50,60,70] bucket: 2: [150,160,170] bucket 3: [250,260,270]
I now want to create a range of numbers that causes these buckets to fall in a certain percentage of that new range of numbers. Essentially what would my new min/max be in order to normalize these values to fall within a certain percentage?
bucket 1 - should now fall between 0-33% of the new range bucket 2 - should now fall between 33-66% of the new range bucket 3 - should now fall between 66-100% of the new range
For example, having a range of 25-350 would satisfy this.
The values in bucket 1 fall between 8-14% of this range The values in bucket 2 fall between 38-48% of this range The values of bucket 3 fall between 69-75% of this range.
Without bringing the range window down from 600 to 350, bucket 3 would've fallen between 39-42% which is not where I need it to be (between 66-100%)
In theory, there would be a wide variety of ranges that can satisfy the requirements, but Ideally, I would like to find the "minimum" range needed to satisfy the requirements. What is the closest min to the original min and the closest max to the original max that will satisfy the conditions?